Another example of the mutual singularity of multifractal measures
DOI:
https://doi.org/10.22199/issn.0717-6279-2021-01-0002Keywords:
Multifractal analysis, Homogeneous Moran fractals, Homogeneous Moran MeasuresAbstract
We propose an example for which the multifractal Hausdorff and packing measures are mutually singular.
References
N. Attia and B. Selmi, “Regularities of multifractal Hewitt-Stromberg measures”, Communication Korean Mathematical Society, vol. 34, no. 1., pp. 213-230, Jan. 2019, doi: 10.4134/CKMS.c180030
N. Attia and B. Selmi, “A multifractal formalism for Hewitt-Stromberg measures”, Journal of geometric analysis, Oct., 2019, doi: 10.1007/s12220-019-00302-3
F. Ben Nasr, I. Bhouri and Y. Heurteaux, “The validity of the multifractal formalism: results and examples”, Advances in mathematics, vol. 165, no. 2, pp. 264-284, Feb. 2002, doi: 10.1006/aima.2001.2025
M. Das, “Pointwise Local Dimensions”, Ph.D. Thesis, The Ohio State University, USA, 1996.
M. Das, “Hausdorff measures, dimensions and mutual singularity”, Transactions of the American Mathematical Society, vol. 357, no. 11, pp. 4249-4268, Nov. 2005. doi: 10.1090/S0002-9947-05-04031-6
Z. Douzi and B. Selmi, “On the mutual singularity of multifractal measures”, Electronical research archives, vol. 28, no. 1, pp. 423-432, Mar. 2020, doi: 10.3934/era.2020024
K. J. Falconer, Techniques in fractal geometry, New York, NY: Wiley, 1997.
T. C. Halsey, M. H. Jensen, L. P. Kadanof, I. Procaccia, and B. J. Shraiman, “Fractal measures and their singularities: the characterization of strange sets”, Physics Revision A., vol. 33, pp. 1141-1151, Feb. 1986, doi: 10.1103/PhysRevA.33.1141
L. Olsen, “A multifractal formalism”, Advances in mathematics, vol. 116, no.1, pp. 82-196, Nov. 1995, doi: 10.1006/aima.1995.1066
L. Olsen, “Dimension inequalities of multifractal Hausdorff measures and multifractal packing measures”, Mathematica scandinavica, vol. 86, no.1, pp. 109-129, 2000, doi: 10.7146/math.scand.a-14284
Y. Pesin, Dimension theory in dynamical systems, Contemporary views and applications, Chicago, IL: University of Chicago Press, 1997.
J. Peyrière, “Multifractal measures,” in Probabilistic and Stochastic Methods in Analysis, with Applications, J. S. Byrnes, J. L. Byrnes, K. A. Hargreaves, and K. Berry, Eds. Dordrecht: Springer, 1992, pp. 175–186.
M. Wu, “The multifractal spectrum of some Moran measures”, Science in China Series A: Mathematics volume, vol. 48, pp. 1097-1112, Aug. 2005, doi: 10.1360/022004-10
Published
How to Cite
Issue
Section
Copyright (c) 2021 Zied Douzi, Amal Samti, Bilel Selmi

This work is licensed under a Creative Commons Attribution 4.0 International License.